Microscopic Insights into Cation-Coupled Electron Hopping Transport in a Metal–Organic Framework

Electron transport through metal–organic frameworks by a hopping mechanism between discrete redox active sites is coupled to diffusion-migration of charge-balancing counter cations. Experimentally determined apparent diffusion coefficients, Deapp, that characterize this form of charge transport thus contain contributions from both processes. While this is well established for MOFs, microscopic descriptions of this process are largely lacking. Herein, we systematically lay out different scenarios for cation-coupled electron transfer processes that are at the heart of charge diffusion through MOFs. Through systematic variations of solvents and electrolyte cations, it is shown that the Deapp for charge migration through a PIZOF-type MOF, Zr(dcphOH-NDI) that is composed of redox-active naphthalenediimide (NDI) linkers, spans over 2 orders of magnitude. More importantly, however, the microscopic mechanisms for cation-coupled electron propagation are contingent on differing factors depending on the size of the cation and its propensity to engage in ion pairs with reduced linkers, either non-specifically or in defined structural arrangements. Based on computations and in agreement with experimental results, we show that ion pairing generally has an adverse effect on cation transport, thereby slowing down charge transport. In Zr(dcphOH-NDI), however, specific cation–linker interactions can open pathways for concerted cation-coupled electron transfer processes that can outcompete limitations from reduced cation flux.


1) General Materials and Experimental Methods
All solvents and chemicals were purchased from commercial suppliers (Sigma Aldrich, VWR, Fluorochem, TCI) and were used without further purification unless otherwise noted. TBAPF6 was recrystallized from EtOH and dried under vacuum prior to electrochemical experiments. 1 H NMR spectra were measured on a JEOL 400 MHz spectrometer at 293K. The chemical shifts are reported in ppm and are internally referenced to the residual solvent peak. Scanning electron microscopy (SEM) images were obtained on a Zeiss LEO 1550 Schottky FEG scanning electron microscope equipped with InLens detector at an acceleration voltage of 3 kV. Surface area and film thickness of each individual film was determined using ImageJ 1 .
Cyclic voltammetry (CV) and chronoamperometry was performed using an Autolab PGSTAT100 potentiostat with GPES 4.9 software (EcoChemie). A 0.5 M solution of electrolyte in DMF, EtOH, or THF was used as the supporting electrolyte. A one-compartment, 3-electrode setup was employed with a glassy carbon (GC) rod counter electrode and a nonaqueous Ag/Ag(NO3) (10 mM in MeCN) reference electrode, referenced to the ferrocenium/ferrocene couple (Fc +/0 ). The counter and reference electrodes were isolated from the main solution by salt bridges with glass frit tips and filled with the supporting electrolyte solution. FTO with solvothermally-grown MOF thin films were employed as the working electrode. Solution-phase measurements of the linker were performed at a 1 mM concentration (unless otherwise noted) in DMF, EtOH, or THF with 0.5 M supporting electrolyte using a GC working electrode (0.071 cm 2 ). Prior to measurements, the solutions were sparged with Ar to remove O2. CVs of MOF-modified FTO were measured in 7 mL of supporting electrolyte solution at a scan rate of 50 mV s -1 . CVs of homogeneous linker were measured in 5 mL of supporting electrolyte solution at a scan rate of 50 mV s -1 .
Synthesis of dcphOH-NDI 2 : 1,4,5,8-Naphthalenetetracarboxylic dianhydride (0.804 g, 3.0 mmol) and 4-amino-3-hydroxy benzoic acid (1.01 g, 6.6 mmol) were added to a 50 mL flame-dried, Ar-purged 2neck RBF fitted with a reflux condenser. The solids were suspended in anhydrous DMF (20 mL). The reaction was stirred in a 145°C sand bath overnight under Ar. The reaction was then allowed to cool to RT, and 5 mL of 1M HCl was added to the solution. The acidified mixture was slowly added to ice cold H2O (250 mL) to precipitate the product as a pale yellow-brown solid. The solids were collected by centrifugation, and the supernatant decanted. The solids were washed sequentially with EtOH (50 mL), H2O (50 mL), and Et2O (50 mL). The resulting solid was dried under vacuum to yield the product as a yellow-brown solid CV and Chronoamperometry of Zr(dcphOH-NDI)@FTO: MOF films not analyzed in DMF were soaked in the solvent of the electrochemical analysis for at least 1 hour to exchange the DMF from the film. After taking a background CV of the electrolyte solution with a glassy carbon disk (0.071 cm 2 ) working electrode to verify the system was purged of O2, a Zr(dcphOH-NDI)@FTO sample was removed from the soaking solvent and dried under a N2 stream. The MOF-modified electrode was then immediately mounted into a sample holder and wrapped with Teflon tape, leaving ~1 cm 2 of MOF thin film exposed. The electrode was then immediately introduced into the degassed electrolyte solution and left to soak for ~10 minutes while continuing to stir and degas the electrolyte. After this soaking period, the MOF film was cycled for 50 CV scans at 50 mV s -1 to equilibrate the film, by which point the current response was stabilized for the final successive scans. For samples analyzed in DMF, CVs showed two distinct redox features corresponding to the NDI 0/•and NDI •-/2couples. From these CVs, a potential lying between the redox couples was chosen to isolate the NDI 0/•redox event for chronoamperometry. For samples analyzed in THF and EtOH, the measured CVs show either one broad redox feature (Li + /THF, Li + /EtOH) or a poorly defined feature (TBA + /THF) in the expected potential window for both the NDI 0/•and NDI •-/2couples. To resolve the two redox events and choose an appropriate potential to isolate the NDI 0/•couple for controlled potential experiments, differential pulse voltammetry (DPV) from 0 V → -1.7 V (unreferenced) was applied with an interval time of 0.1 s, and step potential of 1 mV. Controlled potential experiments were performed by first applying a non-reducing potential (determined from MOF film CVs, generally ~ -0.6 V v. Fc +/0 ) for 90s to ensure the NDI linkers in MOF film are in the NDI 0 state. The potential was then stepped down to an appropriate potential to generate the NDI radical anion (NDI •-) and this potential then held for 900s. The potential was then stepped back to a non-reducing potential for 90s to return the film to a neutral state. After chronoamperometry, 3 consecutive CV scans (scan rate: 50 mV s -1 ) were taken of MOF-modified electrodes to verify stability of film throughout controlled potential experiments.
Cottrell analysis for determination to assess cation diffusion-migration in MOF films: The electroactive concentration of NDI linkers in each MOF thin film and the apparent diffusion coefficient ( ) in the different electrolyte/solvent combinations were determined by chronoamperometry. The data for all analyzed Zr(dcphOH-NDI)@FTO films are shown in Figures S2-S7.
After applying a sufficiently mild potential for 90s to begin with a neutral film, the potential was stepped to an appropriately negative potential to reduce the NDI linkers to the NDI 0/•state and held for 900s. The current density (j) and recorded charge (Q) from this potential step were plotted vs. time to determine the total charge passed. A residual background current can be observed as the recorded charge does not decay to a slope of 0 after an extended time. This background current is subtracted by fitting the linear region of the charge (t = 400-600s after potential step for fits shown). The y-intercept of this linear fit line corresponds to the total charge passed to reduce all electrochemically addressable NDI linkers to the NDI •redox state in the film. The electroactive NDI concentration 3 was calculated according to: Where Γe is the electroactive linker concentration (in mol cm -2 ), Q is the charge (in C), n is the number of electrons involved in the redox event, F is Faraday's constant (in C mol -1 ), and SA is the surface area of the MOF-modified electrode (in cm 2 ). Here, it is assumed that n=1 as the applied potential is chosen to isolate the NDI 0/•couple. SA is independently determined for each sample for accuracy.
To determine for electron-hopping diffusion in each system, the time-dependent current response (here identified as time-dependent current density j(t)) was fitted to the Cottrell equation: Where df is the MOF film thickness (in cm 2 ) and is the diffusion coefficient for charge diffusion in the film (in cm 2 s -1 ). df for each film is measured from SEM images taken after electrochemical measurements. From a plot of j(t) vs. t -1/2 , it is evident that for points corresponding to times shortly after the potential step, a linear trend is observed. These short time points correspond to a regime where the diffusion layer for electron-hopping charge diffusion is small and confined within the film, i.e. where diffusion is semi-infinite. Therefore, by fitting the linear region of this plot, can be extracted from the following relationship: Experimentally determined values of Γe and for each individual film measured in the noted electrolyte solutions are detailed in Tables S2 -S7 below the correspond CV/chronamperometry data and Cottrell analysis. Averaged values for each set of supporting electrolyte solution conditions (n=3) is given in the main text (Table 3). Figure S1. Representative characterizations and measurements of Zr(dcphOHNDI)@FTO. (a) Initial CV cycling of Zr(dcphOH-NDI)@FTO measured in 0.5 M KPF6 in DMF (ν = 50 mV s -1 ), demonstrating redox behavior. CV cycling previously described for these MOF films demonstrated a 'conditioning' effect, with increasing current until a maximum current density was reached. This effect was not typically observed for all films measured in this study, likely due to the film handling prior to electrochemical analysis. For all samples reported here, films were kept solvent-swelled at all times and only dried under a stream of N2 directly before introducing to cell. This treatment likely prevents desiccation of the MOF film that must be 'reswelled' during the initial CV cycling period, leading to improved current responses as a result of optimized pore accessibility due to the likelihood of minimal pore collapse. (b) Image of film before introducing to electrochemical cell. Segment lengths of grid paper measure 0.5 cm. Surface area (SA) determined from this image using ImageJ. 1 (c) SEM image of Zr(dcphOH-NDI)@FTO to verify similarity to previously reported materials. SEM confirms PIZOF morphology of MOF films. Cracks in the film are likely due to desiccation of the MOF film when under vacuum in the SEM chamber, leading to collapse of individual MOF particles comprising film. Films were not sputter-coated. (d) SEM image of cross section of Zr(dcphOH-NDI)@FTO. Film thickness (df) determined from cross section images using ImageJ 1 , with multiple measurements depicted (yellow lines) and averaged for final value of df. Figure S2. Electrochemical data for all Zr(dcphOH-NDI)@FTO samples measured in 0.5 M LiClO4 in DMF. Top row: CV cycling (50 scans) for all samples at scan rate of 50 mV s -1 . Middle row: chronoamperometry (solid red line) and chronocoulometry (solid black line) after stepping the potential to isolate the NDI 0/•redox couple for each sample (selected from corresponding CVs, generally ~ -0.67 V → -1. 22 V v. Fc +/0 ). The total charge passed after complete reduction for each sample was determined after subtracting a residual background current (red dashed line). Blue boxes illustrate the window of time points chosen for linear fits. Bottom row: Cottrell plots of MOF film samples after potential step. Linear fits are shown by red dashed lines, and blue boxes illustrate the window of points selected for linear fits.

4) Three-dimensional electron diffraction measurements
Samples were prepared by dispersing solvothermally-prepared bulk Zr(dcphOH-NDI) in ethanol, which was then gently mortared and drop-cast onto a copper grid covered in a holey carbon film. The sample was loaded into a Gatan 914 cryo transfer holder, which was then cooled to approximately 200 K before being inserted into the TEM column. Three-dimensional electron diffraction (3DED) data were collected using a JEOL JEM-2100 TEM at 98 K, equipped with a Timepix detector from Amsterdam Scientific Instruments, while continuously rotating the crystal at 0.45° s −1 . The experiment was carried out using Instamatic, 4 with data reduction performed in XDS. 5 The acquired intensities were then used to solve the structure of SU-102 with SHELXT, 6 and refined using SHELXL, 7 with electron scattering factors extracted from SIR2014. 8 From the 3DED data, all non-hydrogen atoms could be located in the initial structure solution.  Due to the potential for positional disorder of the hydroxyl groups on the carboxylate-bearing phenyl rings of the dcphOH-NDI linker during diffraction measurement, the structure model of the MOF indicates a partial occupancy for each likely position of these hydroxyl groups (50% each). Because the diffraction data shows this single hydroxyl is equally likely to be located on either side of the phenyl spacer, the structures shown in Figure 2 show only one hydroxyl group on each phenyl ring for visual clarity. Figure S9. Comparison of PXRD patterns between the simulated powder pattern for Zr(dcphOH-NDI) as determined by 3DED (bottom, dark grey), a simulated powder pattern of tin oxide (middle, light grey) and the experimental powder pattern of Zr(dcphOH-NDI)@FTO (top, blue).

System Setup
To simulate the cation ions diffusion in different solvents, we set up a fully reduced Zr(dcphOH-NDI) system. The geometrical structure was cut from the 3 × 3 × 3 UiO-66 9 units. Then, the linker of the crystal structure of UiO-66 were substituted with the NDI-based Zr(dcphOH-NDI) linker. Subsequently, the interpenetrated framework model was built by putting part of the obtained geometrical structure into its duplicate structure. Acetate ions were used to saturate the terminate sites of the systems. The Zr 4+ in the metal cluster of Zr(dcphOH-NDI) were described by our published dummy atom model. 10 The parameters of NDI, oxygen, hydroxyl ligands, TBA and solvent molecules dimethylformamide (DMF) and tetrahydrofuran (THF) were taken from the General Amber Force Field (GAFF2) force field. 11 The partial atomic charges of NDI and TBA were obtained by the restrained electrostatics potential (RESP) 12 method at the level of B3LYP/6-31G* 13 . The RESP charges of DMF and THF molecules were calculated at B3LYP/6-31G* level with the corresponding polarizable continuum model (CPCM) 14 as the solvent environment.
The Zr(dcphOH-NDI) model as shown in Figure S10 was solvated in DMF or THF solvent box with the edge extend to 10 Å from the frameworks, giving a box with the size 100Åx90Å x110Å. Then, for each solvent box the systems were neutralized with K + , Li + and TBA + cations, respectively. In order to compare the binding affinity between cation and the reduced NDI in different solvents, a series of models containing one reduced NDI and respective cations were built (illustrated in Figure S11. Then, the models were solvated by pre-equilibrated DMF or THF boxes giving a rectangular solved box with 20 Å from the solute molecules to the edge of the box. Solvation processes were performed by using the LEaP module in AmberTools. 15 Periodic boundary conditions (PBC) are used for all of our MD simulations. Figure S10. Graphical representation of the Zr(dcphOH-NDI) PIZOF model that was used in MD simulations for cation distribution. Figure S11. Individual singly reduced NDI linkers with different cations (Li + , K + , and TBA + ) used for the potential of mean force simulations to estimate the binding free energies of the ions to the reduced linkers in different solvents.

MD simulation
MD simulations were performed and analyzed using the AMBER16 and AmberTools packages. 15 For all of the solved systems, two stages energy minimization were implemented: first, the solvent molecules were minimized by constraining the solute molecules, and then the whole system was minimized using 5000 steps steepest conjugate and another 5000 steps for conjugate gradient. The systems were then heated from 50 to 300 K under the NVT (constant volume and temperature) ensemble in 50 ps, after which a 200 ps density equilibration MD simulation was performed under the NPT (constant pressure and temperature) ensemble for each of the systems. During the density equilibration, the Langevin thermostat 16 and Berendsen barostat 17 with a collision frequency of 2 ps and a pressure relaxation time of 1 ps were used to control the target temperature and pressure to 300 K and 1.0 atm. Thereafter, productive NPT MD simulations were performed for 30 ns and 5 ns for UiO-NDI and one-linker systems, respectively. From the last snapshot of the 5 ns MD simulations, a series of 500 ps steered MD simulations were performed to generate trajectories along the binding of cations to the reduced NDI molecule. With the obtained snapshot, umbrella sampling simulations were carried out with 0.25 Å windows separation to obtain the binding free energy profile between cations and the reduced NDI. The weighted histogram analysis (WHAM) method was used to generate the potentials of mean force. [18][19][20]

Simulation Results and Discussion
The measured experiment shows the cation diffusion (DI) between different cations in same solvent only have 2-4 times different. To understand the movement difference between different cations and the effects of solvents on this movement, we performed a series of MD simulations. First, we analyzed the diffusion of cations to the reduced linkers of Zr(dcphOH-NDI).
We find that the ions bind somewhat differently to the linkers, where Li + and K + preferentially interact with the oxygen atoms of the NDI while TBA + interacts in a less specific manner ( Figure S12).
To illustrate the movement of cations in different solvents, we measured the variation of the number of ions within a distance (3 Å for Li + , 3.5 Å for K + and 4 Å for TBA + ) of an imide-oxygen center of the NDI linker ( Figure S13) with the simulation time. In both DMF and THF solvents, Li + and K + quickly bind (less than 2 ns) with the reduced NDI, whereas the TBA + needs a longer time (~10 ns) to fully associate with all the NDI linkers. This is likely due to the larger volume and the shielded charges on TBA + . In DMF, the number of binding Li + is slightly higher than that of K + , but after 5 ns they both have lower binding numbers than TBA + . This effect is caused by TBA + having long side chains that bring the cation within the 6 Å distance of the NDI-O.  In THF solvent, the number of binding cations is much higher than that in DMF solvent, and both Li + and K + show stronger binding interactions with the linkers. Note that, although the experimental data for diffusion of K + in THF is not available, we simulated K + here for comparison. The radial distribution function (RDF) of cations among the NDI (Figure S14) clearly show that more Li + than K + are associated to the NDI in both DMF and THF solvents, and from the integral of RDF we see values that less than ¼ (there are four NDI oxygens per counter ion) indicating a distribution of bound and free ions. In THF, the ions are much more tightly bonded as indicated by the higher peak in the RDF of both K + and Li + , and the integral which is approximately ¼ which corresponds to all cations bound. To quantify the difference in the interaction free energy between the different cations to the NDI in the different solvents we performed the potential of mean force (PMF) calculations for the isolated linkers (but with the carboxylates replaced by hydrogen atoms). We observe a barrier for the dissociation of Li + and K + which is related to solvent rearrangement as the cation-O distance increases ( Figure S15) The free energy barrier for dissociation of Li + in THF is about 8.0 kcal/mol whereas in DMF the value decreased to about 5.2 kcal/mol. For K + , the free energy barrier is 5.0 kcal/mol in THF and 3.0 kcal/mol in DMF. TBA + shows a qualitatively different behavior and the dissociation free energy does change much as the solvent is changed. Figure S15. Potential mean force of cations binding with the reduced NDI. Note that the free energy increase for K + in THF solvent at distance longer than 8 Å was because the cation moves to another side of NDI and bonded with another NDI oxygen.

DFT setup for single cluster with two linkers
One Zr6O4(OH)4 cluster with 12 linkers was cut out from an MD trajectory. All except two linkers were replaced by acetate ions, and the ends of the two remaining linkers were neutralized with one proton each. The structures were fully optimized with the positions of the two terminal -COOH carbons restrained at the original position to simulate the constraints from the framework. The geometry optimizations were performed using the Jaguar 11.0 software package by Schrödinger 21 and the B3LYP-D3 functional 13,22 and dispersion correction with the LACVP** basis set and corepotential for the metal atoms. The once reduced species without counterions was set up as an anionic species with a spin multiplicity of 2, and the geometry was optimized. The three ions were then placed at positions similar to the ones observed in the MD and the structure was optimized, giving a system neutral charge and multiplicity of 2. For the spin density calculations we included the PBF solvation model in Jaguar to account for solvent polarization. We used standard settings for dimethyl formamide. In Figure 8 the spin densities of the Li + associated species is shown on the left, while the TBA+ associated species is shown on the right. Since charge delocalization can be exaggerated for some functionals we performed the calculation with the BHandHLYP functional, as well as the range separated b97x functional. Both gave results that were close to identical to B3LYP with the unpaired electron localized on one linker for the TBA + system and delocalized over two linkers for the Li + system.